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Showing papers on "Bicubic interpolation published in 1973"


Journal ArticleDOI
01 Jun 1973
TL;DR: In this article, the authors examined the relative merits of finite-duration impulse response (FIR) and infinite duration impulse response(IIR) digital filters as interpolation filters and showed that FIR filters are generally to be preferred for interpolation.
Abstract: In many digital signal precessing systems, e.g., vacoders, modulation systems, and digital waveform coding systems, it is necessary to alter the sampling rate of a digital signal Thus it is of considerable interest to examine the problem of interpolation of bandlimited signals from the viewpoint of digital signal processing. A frequency dmnain interpretation of the interpolation process, through which it is clear that interpolation is fundamentally a linear filtering process, is presented, An examination of the relative merits of finite duration impulse response (FIR) and infinite duration impulse response (IIR) digital filters as interpolation filters indicates that FIR filters are generally to be preferred for interpolation. It is shown that linear interpolation and classical polynomial interpolation correspond to the use of the FIR interpolation filter. The use of classical interpolation methods in signal processing applications is illustrated by a discussion of FIR interpolation filters derived from the Lagrange interpolation formula. The limitations of these filters lead us to a consideration of optimum FIR filters for interpolation that can be designed using linear programming techniques. Examples are presented to illustrate the significant improvements that are obtained using the optimum filters.

643 citations


Book ChapterDOI
01 Jan 1973
TL;DR: Boneva, Kendall and Stefanov as discussed by the authors rediscovered the essential features of what I like to call cardinal cubic spline interpolation, but the data are not the usual function values that are to be interpolated, but rather approximations of the derivative (i.e. the unknown density function) in the form of a histogram.
Abstract: In [3] Boneva, Kendall and Stefanov (B.K.S.) have effectively rediscovered the essential features of what I like to call cardinal cubic spline interpolation. Moreover, and this is an important point, the data are not the usual function values that are to be interpolated, but rather approximations of the derivative (i.e. the unknown density function) in the form of a histogram. This (pershaps only apparent) difference is bridged by the ingenious area-matching condition.

42 citations


Journal ArticleDOI
TL;DR: In this paper, the authors gave explicit error bounds for bicubic spline interpolation and gave similar bounds for the cubic spline-blended interpolation scheme of Gordon.

37 citations


Journal ArticleDOI
TL;DR: In this paper, error bounds for lacunary interpolation of certain functions by deficient quintic splines are extended to a wider class of functions and a stability result for such interpolation is also presented.
Abstract: In the previous paper by A Meir and A Sharma, error bounds for lacunary interpolation of certain functions by deficient quintic splines are developed In this note, we extend their results to a wider class of functions and indicate that the extended results are best possible In addition, a stability result for such interpolation is also presented

16 citations


Journal ArticleDOI
TL;DR: In this article, a parametric discrete element based entirely on bicubic Hermite polynomials is proposed for plate bending and plate stretching problems, which are in good agreement with closed-form solutions and photoelastic results in the case of a stress-concentration problem.
Abstract: A limitation of most plate and shell discrete elements now in use is the shape of their undeformed geometry Typically, the plan form of these elements is a straight-sided triangle or quadrilateral that linearly approximates the undeformed geometry while often using higher-order polynomials to approximate the deformed geometry This modelling difference leads to inefficiencies that can be eliminated, as demonstrated by a new parametric discrete element based entirely on bicubic Hermite polynomials This representation of element geometry corresponds to the bicubic Coon's surface patch widely used in design, which allows a common mathematical model for design and analysis Consideration is given to automating the generation of these patches Solutions are presented for several plate bending and plate stretching problems The solutions are in good agreement with closed-form solutions and photoelastic results in the case of a stress-concentration problem These data demonstrate that the new parametric discrete element maintains solution accuracy for plates with curved boundaries

6 citations


Journal ArticleDOI
TL;DR: The bicubic spline approximation defined over a two-dimensional region is obtained using the methods of dynamic programming, avoiding the difficulties of large storage and high dimensionality.

6 citations


Journal ArticleDOI
TL;DR: In this article, the existence of convergent bicubic spline interpolation schemes for non-rectangular domains was confirmed for L-shaped domains, and it was shown that ∥sf − f ∥ = O(hr) where sf is the bicUBic splines interpolant associated with a smooth function f, h is the maximum mesh spacing, r − 4 for uniform partitions, and r = 3 for nonuniform partitions.

4 citations


Journal ArticleDOI
Changhwi Chi1
TL;DR: The currently available bicubic spline fit interpolation scheme for the rectangular coordinate system is not suitable for use with a polar grid pattern and must therefore be modified and a feature of physical significance has been added.
Abstract: Modification of the rectangular bicubic spline fit interpolation scheme so as to make it suitable for use with a polar grid pattern. In the proposed modified scheme the interpolation function is expressed in terms of the radial length and the arc length, and the shape of the patch, which is a wedge or a truncated wedge, is taken into account implicitly. Examples are presented in which the proposed interpolation scheme was used to reproduce the equations of a hemisphere.

3 citations


Journal ArticleDOI
TL;DR: In this paper, the Slater-Koster interpolation method is used to find the explicit form of the matrix elements of the Hamiltonian between Bloch functions and so make possible the calculation of the energy bands in crystals with a cubic structure of perovskite type.
Abstract: The Slater-Koster interpolation method is used to find the explicit form of the matrix elements of the Hamiltonian between Bloch functions and so make possible the calculation of the energy bands in crystals with a cubic structure of perovskite type. In the nearest-neighbors approximation the energy matrix contains 23 independent parameters. The obtained formulas can be applied to a wide class of substances with the stated structure.

3 citations


Journal ArticleDOI
TL;DR: Following four important papers on Birkhoff interpolation by Turan and his associates as discussed by the authors, the following theorems were proved by the following authors: [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15] and [16].
Abstract: Following four important papers on Birkhoff interpolation by Turan and his associates ([2], [3], [4], [14]), Kis ([8], [19]) proved the following theorems.

2 citations


Journal ArticleDOI
TL;DR: Among global interpolation techniques, bicubic splines and spline-blended are reviewed; among local, Hermite's and'serendipity' polynomials, the conclusion is that spline interpolation is most convenient for regular hyper-elements, while high precision finite elements become convenient for very fine or irregular partition as discussed by the authors.
Abstract: Interpolation techniques are reviewed in the context of the approximation of the solution of boundary value problems. From the variational formulation, the approximation error norm is related to the interpolation error norm. Among global interpolation techniques, bicubic splines and spline-blended are reviewed; among local, Hermite's and ‘serendipity’ polynomials. The corresponding interpolation error norms are computed numerically on two test functions. The methods are compared for accuracy and for number of operations required in the solution of boundary value problems. The conclusion is that spline interpolation is most convenient for regular hyper-elements, while high precision finite elements become convenient for very fine or irregular partition.

01 Jun 1973
TL;DR: Two CDC 3800 FORTRAN subroutines (BICUB1 and BICUB2) which perform bicubic spline interpolation of a tabulated function of two variables are described in this paper.
Abstract: : Two CDC 3800 FORTRAN subroutines (BICUB1 and BICUB2) which perform bicubic spline interpolation of a tabulated function of two variables are described. Given the values X(1),...,X(N) and Y(1),...,Y(M) of two independent variables and the corresponding function values U(I,J)=f(X(I), Y(J)), I=1,...,N and J=1,...,M and certain normal derivatives (optional) along the boundaries of the x-y mesh, BICUB1 estimates the derivatives f(x), f(y), and f(xy) at each (I, J) mesh point. If the normal derivatives along the mesh boundaries are unknown, BICUB1 estimates them using a moving third order two dimensional Lagrange interpolating polynomial. Given the coordinates (XPT, YPT) and the derivatives calculated by BICUB1, BICUB2 obtains the coefficients of the bicubic polynomial for the rectangular region of the mesh containing (XPT, YPT) and estimates the functional value UPT=f(XPT,YPT). In effect, the routines pass a twice continuously differentiable piecewise bicubic polynomial, u(x,y) belongs to (C sup 2), through the given functional values.

Journal ArticleDOI
01 Mar 1973
TL;DR: In this paper, the union of two interpolation sets for a regular commutative convolution measure algebra is not necessarily an interpolation set, while every singleton is a Ditkin set.
Abstract: These are proved : (l)The union of two interpolation sets for a regular commutative convolution measure algebra is not necessarily an interpolation set. (2) There exists a regular com- mutative convolution measure algebra for which interpolation sets are not necessarily of spectral synthesis, while every singleton is a Ditkin set. (3) For every nondiscrete LCA group G, there exist compact interpolation sets for M(G) whose union is not an inter- polation set. A tensor algebra method is used.